Introduction to Hedge Funds

Neil A. Chriss, December 1998

Banking and Finance G63.2751

Summary of Lecture

This lecture will define what hedge funds are, discuss
some of the key strategies that hedge fund managers employ and will introduce
some of the important vocabulary and quantitative tools used by hedge fund
managers. The accompanying reading for this lecture is Hedge Funds Demystified:
Their Potential Role in Institutional Portfolios. I thank the Pension
and Endowment Forum of Goldman Sachs & Co. for kindly granting permission
for me to reproduce this document for use by the class. A portion of this
lecture is drawn from this document.

Types of Investment Funds

There are many types of investment funds besides hedge
funds, and to place hedge funds more precisely in the broader context of
different funds, it is a good idea to define several other sorts of funds.
In this section we will talk about:

Mutual funds

Pension funds

Hedge funds

Mutual Funds

Mutual funds are actually investment companies, that is,
they are firms that collect investments from investors and professionally
invest money on behalf of investors. Investment companies collect fees
from investors, usually drawn directly out of the investment, as a fee
for the service of investment. There are primarily three types of fees
an investment company will charge:

Up-front fees: these are fees charged for the
collection of assets. In the world of mutual funds, these are often
known as sales loads.

Management fees: these are fees charged for the
on-going service of investing assets.

Performance fees: these fees are a "cut"
of the profits of investing. Performance fees are assessed on the "upside"
portion of the fund value, that is, on the portion of the value of the
fund due to investment return. For example, if an investor invests $100
in a fund and the fund value rises to $120, then a performance fee may
be charged on the $20 upside.

Mutual funds come in two varieties: closed end and open
end. Open end mutual funds are investment companies that continually offer
new shares of the fund to the public for investment and stand ready to
redeem outstanding shares at the net-asset value (NAV) of the fund.
In this sense, the company is the unique market maker of shares in the
company. They will sell or buy the shares every day. Mutual funds sell
their shares at the fund net-asset value per share, which may be
regarded as the value of the investment in the fund. It is calculated by
taking the value of all investments in the fund less any liabilities (such
as fees) divided by the total number of outstanding shares.

Mutual funds are regulated investment companies. In particular,
they are regulated by the Investment Company Acts of 1940 and 1970. The
1940 Act regulates certain aspect of a fund's operations including financial
statements, investment goals, personnel, debt, and managers. The 1970 Act
regulates sales charges (i.e., sales load and in particular the
maximum sales load) and fees of mutual funds. The main point that
concerns us in this lecture is that mutual funds are tightly regulated
entities, a fact which is not the case for hedge funds.

Note that open end mutual funds cannot be traded in a
secondary market. Their values are determined by the investment company
(mutual fund company) and the company is required (by the Act) to buy and
sell the shares of the company at the NAV. Two key pieces of terminology
concerning all funds are:

Inflows: this is the flow of money into a fund

Outflows: this is the flow of money out of a fund

Closed-end mutual funds unlike open end funds are
traded in a secondary market. Such funds are distinct from open end funds
and work as follows. The fund issues a limited number of shares and does
not redeem the shares. Rather, the company publishes information about
its NAV and the shares are traded on a secondary market or through an over-the-counter
market. In this sense, investors purchases shares of closed end funds much
in the same way they purchase shares of stock and for similar reasons.
An important feature of closed end funds is that their market values
and net-asset values may differ. This is because the net-asset
value, determined by the value of the investments in the fund, may be different
than the value (per share) that investors are willing to pay for the fund.
A closed-end fund whose market value is less than its NAV is said to be
trading at a discount.

Pension Funds

A pension fund is an investment company that manages the
assets of employees of a company and disburses the assets to employees
upon retirement. Contributions to the fund by both employer and employee
finance the pension fund assets. There are two main types of pension
funds:

Defined Benefit: these funds manage their assets
and set their investment goals according to a set of guidelines that define
the type of payouts they will make to employees after retirement.

Defined Contribution: these funds manage their
assets according to a defined set of rules of how an employer's contributions
to the fund are to be made.

I bring up pension funds in this lecture for two reasons.
First, they are a type of investment fund and therefore knowledge of them
helps to reduce confusion about what and what not a pension fund is, and
second, pension funds are large investors in hedge funds. Moreover, the
pension industry has been growing world wide for some time; as a result
has an impact on capital markets, as expressed in the following quote:

Institutional investors can influence the demand for capital-market
instruments in several ways: by increasing the total supply of saving,
by influencing the rest of the personal sector's portfolio distribution
between bank deposits and securities, and via the institutions' own portfolio
choices.

Pension Funds, E. P. Davis, Oxford 1997

Another point concerning the relationship between hedge
funds and pension fund investment is the need for financial innovation,
as Davis points out:

The process of financial innovation-the invention and
marketing of new financial instruments which repackage risk or return streams-has
been closely related to the development of pension funds.

Pension Funds, E. P. Davis, Oxford 1997

Pension funds are often referred to as pension plans,
and the organizations that establish pension plans (such as private or
public companies) are referred to as "plan sponsors". US Pension
funds are regulated by the important ERISA Act of 1974 (Employee Retirement
Income Security Act), and this has implications on how the monies coming
from a pension fund can be invested, how they are to be disbursed, as well
as the financial and fiduciary standards of many of the participants in
the pension plan world. We can only briefly discuss ERISA here, but the
full text of the act can be found on the internet at http://www.benefitslink.com/erisa.

The act begins with the following statement:

The Congress finds that the growth in size, scope, and
numbers of employee benefit plans in recent years has been rapid and substantial;
that the operational scope and economic impact of such plans is increasingly
interstate; that the continued well-being and security of millions of employees
and their dependents are directly affected by these plans; that they are
affected with a national public interest; that they have become an important
factor affecting the stability of employment and the successful development
of industrial relations; that they have become an important factor in commerce
because of the interstate character of their activities, and of the activities
of their participants, and the employers, employee organizations ... that
owing to the lack of employee information and adequate safeguards concerning
their operation, it is desirable in the interests of employees and their
beneficiaries, and to provide for the general welfare and the free flow
of commerce, that disclosure be made and safeguards be provided with respect
to the establishment, operation and administration of such plans; that
they substantially affect the revenues of the United States because they
are afforded preferential Federal tax treatment; that despite the enormous
growth in such plans many employees with long years of employment are losing
anticipated retirement benefits owing to the lack of vesting provisions
in such plans; that owing to the inadequacy of current minimum standard,
the soundness and stability of plans with respect to adequate funds to
pay promised benefits may be endangered ...

Summarizing the US governments reasons for regulating
the pension plan industry, we see:

Pension plans are vital to the welfare of the US economy

Profit on capital gains in pension plans receive preferential
tax treatment and therefore affect the tax revenue of the US government

The second point is important for investment funds: ERISA
money, that is, monies invested by pension plans, receives different tax
treatment vis-a-vis capital gains. Moreover, pension plans have three alternatives
with regard to how they manage their assets:

Manage the pension assets itself

Distribute the pension assets to external money
managers

Use a combination of the first two

Two important points when comparing pension funds as investors
in hedge funds versus individuals as investors in hedge funds are 1) fees
and 2) tax treatment. Pension funds typically pay fees for assets under
management that are well below standard hedge fund fees. For example, Frank
Fabozzi in Investment Management (Prentice Hall, 1995) reports that
a study in 1991 found that public pension funds pay an average of .31%
(31 bps) to have their external assets managed (that is, they pay .31%
of total assets under management as management fee) and private pension
funds pay .41% (41 bps).

As such, pension funds have different investment goals
relative to individual investors. As many hedge funds draw from pension
plans for investment capital, understanding the investment goals and rules
of pension plans is an important aspect of hedge fund marketing.

More on Tax Treatment of Pension Funds

The following brief discussion on tax treatment of pension
funds is taken from Pension Funds, E. P. Davis, Oxford 1997. Broadly
speaking there are three different ways a pension fund can be taxed, depending
on which part of the pension monies are taxed. From this point of view,
pension money is divided into three pieces: contributions (the money going
into the fund) and income (the increase in the funds value due to asset
appreciation), and benefits (the money coming out of the fund to pay employees
upon retirement, or withdrawal from the plan). Each piece may either be
exempt (E) or taxed (T).

Exemption of contributions and income, but taxation
on benefits (EET)

Taxation of contributions only (TEE)

Taxation of benefits only (EET)

A contribution to a pension plan is said to be tax free
if the income to the individual or employer that goes to the pension fund
is not taxed. For example, suppose a US employee makes $50,000 per year
and contributes $2,000 to his or her pension fund in a given tax year.
If this contribution is tax free, then the employee's taxable income that
year is $48,000.

The US follows what is basically an EET taxation plan
for pension funds, though there are limits on the level of tax-free contributions
for DC plans. Such contributions are limited to $30,000 per annum. For
DB plans, the amount of benefits that may be paid to an individual is limited
to an "indexed ceiling", that is, the maximum level increases
with a pre-defined index level.

Most countries globally follow an EET-like plan. The following
table may be of interest:

Investment Implications

Depending on the particular taxation rules applied to
a hedge fund, the plan sponsor will view various investment styles differently.
For example, if a government taxes realized income on capital gains (i.e.,
Australia) then a high turnover investment strategy (i.e., lots of capital
gains) would be tax-disadvantageous to a pension fund. In the US, due to
the EET approach to taxation, capital gains are not taxed, and plan sponsors
do not have to look for "tax efficient" investment strategies.

Hedge Funds

The first thing to know about hedge funds is that the
term hedge fund is not a legal term, but rather an industry term.
What a hedge fund is, therefore, is subject to some amount of interpretation.
Consider a few definitions. From Wall Street Words Houghton &
Miflin 1997:

A very specialized, volatility open-end investment company
that permits the manager to use a variety of investment techniques usually
prohibited in other types of funds. These techniques include borrowing
money, selling short and using options. Hedge funds offer investors the
possibility of extraordinary gains with above average risk.

From Hedge Funds Demystified, Goldman Sachs &
Co.:

The term "hedge fund" includes a multitude
of skill-based investment strategies with a broad range of risk and return
objectives. A common element is the use of investment and risk management
skills to seek positive returns regardless of market direction.

From the VAN Hedge Fund Advisors International web page:

A U.S. "hedge fund" usually is a U.S. private
investment partnership invested primarily in publicly traded securities
or financial derivatives.

From the Hennessee Group LLC Web page:

A hedge fund is a "pool" of capital for accredited investors
only and organized using the limited partnership legal structure... the
general partner is usually the money manager and is likely to have a very
high percentage of his/her own net worth invested in the fund.

As you can see, the definitions above focus on several
aspects of investment companies known as hedge funds:

legal structure

investment strategy

investor pool

All three components are important in understanding hedge
funds. To go further let's discuss first what hedge funds are and what
some of their salient features are:

Hedge funds are legally limited partnerships.

Hedge funds are unregistered (i.e., unregistered with
the SEC) investment companies. That is, they are not regulated by the SEC
(more on this later).

Hedge funds can be users of a variety of investment strategies
and products, including options, future, swaps and short selling.

Hedge funds often employ leverage, in that the amount
of notional market exposure often exceeds the investment capital of the
fund.

Hedge funds have limited liquidity. Typically
investors can only get into funds on certain dates and can only get their
money out of funds on certain dates.

Who invests in hedge funds?

Wealthy individuals. For an individual to invest
in an unregistered investment company, the SEC must deem an individual
to be an accredited investors (a defined by SEC rule 501 of Regulation
D. The full text of this rule may be found at http://www.solarattic.com/rule501.htm).
The rule includes the following points for an individual:

The individual must have at the time of investment a
net worth (or joint net worth with spouse) exceeding $1,000,000, or

The individual must have individual income exceeding
$200,000 in each of the two most recent years or joint income with spouse
exceeding $300,000 in each of the two most recent years, and must
have a "reasonable expectation" of reaching the same level in
the coming year.

And the rule contains the following points for an organization,
corporation or other such entity:

The organization must have total assets in excess of
$5,000,000, or

The organization's owners must be accredited investors.

Endowments, e.g., the Wall Street Journal (December
8, 1998) and others report that the University of Pittsburgh made a $5
million investment in Long Term Capital

The University of Michigan hired four hedge fund managers
to manage $100m of its $2.5bn pension fund, and P&I reports that University
of Michigan has a total of about $300m invested with hedge funds.

Other Hedge Funds: Some hedge funds invest in
other hedge funds, including offering Funds of Funds, that is, they
strategically allocate their capital to other funds. Pension and Investments
(November 30, 1998) reports that Grosvenor Capital Management invested
$7m in Long Term Capital Management:

One important item that none of the definitions covered
was hedge fund fee structures, which is, in my opinion, a key distinguishing
feature of hedge funds versus in particular mutual funds. Hedge funds almost
always have a fee structure that includes both a fixed fee and a management
fee. The fixed fee usually ranges between 1 and 2% of assets under management
and the management fee ranges between 20 and 25% of upside performance.
As hedge funds are unregulated, these ranges are often exceeded, and can
be as high as 5% fixed fee and 25% management fee. Hedge fund fees are
often quoted in language such as "2 and 20" meaning 2% fixed
fee and 20% management fee. There are two additional important points about
hedge fund fees:

the benchmark

high water mark

The performance fee is sometimes calculated net of a benchmark.
That is, the returns that fees are paid on are sometimes only those returns
in excess of some benchmark. Sometimes the benchmark is a risk-free interest
rate such as LIBOR (often called the cash benchmark, meaning performance
fees are paid on the profit that would be made in excess of an investment
in cash) and other times it is a market index such as the MSCI World Index
or the S&P 500 index.

Example: Suppose at the beginning of year 1 a hedge
fund has a net asset value of 100, and throughout the year the fund realizes
a 25% return, raising the net asset value to 125. Then if an investor entered
the fund with a $1,000,000 investment at the beginning of year 1 then his
or her "shares" would be worth $1,250,000 gross of fees. If
the benchmark was cash, say 5%, then the fees would be paid on the
$200,000 upside in excess of cash. That is, the first 5% of the return
would not have to have fees paid on it. If the fees were 2 and 20, then
the investor would pay $20,000 in fixed fee (2%) and 20% of the upside
above cash, that is, an additional $40,000 for a total of $60,000 in fees.
This would make the investment value, gross of fees, equal to $1,190,000.

The high water mark is an important concept: investors
in hedge funds enter the fund at a certain net asset value, which we'll
call the entering NAV. If the fund loses money in a given year and then
makes back that money in a subsequent year, the investor is usually not
required to pay a management fee on any portion of the upside in the subsequent
year that was below the entering NAV.

Example: Suppose an investor enters a hedge fund
with a $1,000,000 at the beginning of year 1, and in that year the fund
is down 20%, that is, the value of the investment drops to $800,000 gross
of fees. The investor still pays the management fee (that is why it is
called a fixed fee), but the investor pays no management fee. Now suppose
that after year two the investment value is up to $1,200,000, representing
over a 30% gain in year two for the fund. The investor, nevertheless, only
pays a management fee on $200,000, that is, he or she only pays a fee on
the amount in excess of the entering NAV. The entering NAV in this case
is called the high water mark. In subsequent years if there is a
drop in NAV, the new high water mark will be the entering NAV of the previous
year, or the previous high water mark, whichever is greater.

Liquidity

Hedge funds, unlike mutual funds, are not able to stand ready
to buy and sell shares on any given date. Rather they have two forms of
liquidity constraints that they impose on investors:

Liquidity dates

Lockup

Minimum investment

Liquidity dates refer to pre-specified times of the year
when an investor is allowed to redeem shares. Hedge funds typically have
quarterly liquidity dates, but yearly liquidity dates are not unheard of.
Moreover, it is often required that investors give advanced notice of the
desired to redeem: these redemption notices are often required 30 days
in advance of actual redemption. Here is a quote from the November 16,
1998 issue of Pension & Investments, commenting on hedge fund redemptions:

Judgement day looms for hedge fund managers as they ponder
the possibility of mass redemptions following market volatility and recent
hedge fund failures.

Since most U.S. hedge funds allow redemptions only at
year end, and require a minimum 30-day notice, hedge fund managers find
themselves on the cusp of the redemption period not knowing what to expect.

Offshore hedge funds, which are more liquid than their
U.S. counterparts, already have experienced relatively large redemptions.Hedge funds fear redemption season, Pension &
Investments November 16, 1998

Lockup refers to the initial amount of time an investor
is required to keep his or her money in the fund before redeem shares.
Lockup therefore represents a commitment to keep initial investment in
a fund for a period of time. Once the lockup period is over, the
investor is free to redeem shares on any liquidity date. The length of
the lockup period represents a cushion to the hedge fund manager, especially
a new one. If the hedge fund is unlucky enough to experience a drawdown
(a sharp reduction in net asset value) after the launching of his or her
fund, then the lockup period will force investors to stay in the fund rather
than bail out. The ability for a hedge fund to demand a long lockup period
and still raise a significant amount of money depends a great deal on the
quality and reputation of the hedge fund as well as the market savvy of
the marketers of the fund. For example, Long Term Capital Management was
able to require a three year lockup from investors. The Wall Street Journal
in How Salesmanship and Brainpower Failed to Save Long-Term Capital
November 16, 1998 reports that John Meriwether, manager of Long Term
Capital

... wanted some stiff restrictions. He insisted that investors
not be allowed to withdraw money for at least three years (Most hedge funds
allow investors to withdraw annually, and in some cases quarterly.) The
fund also required a $10 million minimum - one of the highest in the industry.

Then there were the sky-high fees: an annual management
charge of 2% of assets, plus 25% of profits, compared with 1% and 20% respectively,
for most of the industry.

Legal Structure

U.S. hedge funds are structured as limited partnerships.
A limited partnership is characterized by the fact that it has two
types of partners:

General partners (GP's)

Limited partners (LP's)

Limited partners have limited liability with respect to
the creditors of the partnership. In other words, the extent of the liability
of a limited partner is the partner's investment. In the context of hedge
funds, limited partners buy shares in the "corporation" (the
hedge fund) and the value of the shares, gross of fees, are tied to the
net asset value of the fund. In practical terms, the general partners run
the hedge fund. They are often referred to as the hedge fund manager. The
limited partners are the investors.

The Hedge Fund Industry

It is important to understand the magnitude of
the hedge fund industry and the sizes of some of the key players in the
industry. "Hedge Funds Demystified" estimates that the size of
the whole industry is approximately $400bn, and that the investor pool
is dominated by wealthy individuals (accredited investors), with pension
fund interest increasing. "Hedge Funds Demystified" also notes
that it is difficult to accurately assess the size of the industry, so
this number should be read as mainly an indication of the order of magnitude.
To get a sense of where this stands, consider the pension fund industry
by contrast. Davis, in Pension Funds, reports that as of year end
1991, the US pension fund industry's assets were at least $2.9 trillion.
In other countries, the number was less for two reasons: the pension fund
industry contributes less assets as a percentage of GDP than the US (except
Germany and Switzerland) and the US GDP is much larger than other countries.
Nevertheless, the global pension fund industry (as of year end 1991) was
estimated at approximately $4.2 trillion. The numbers since then have surely
grown, but I currently do not have more up-to-date numbers.

Types of Hedge Funds

Hedge funds are generally classified according to the
type of investment strategy they run. Below we review the major
types of strategies, but refer members of the class to "Hedge Funds
Demystified" for greater detail.

Market Neutral (or Relative Value) Funds

Market neutral funds attempt to produce return series
that have no or low correlation with traditional markets such as the US
equity or fixed income markets. Market neutral strategies are characterized
less by what they invest in than by the nature of the returns. They often
are highly quantitative in their portfolio construction process, and market
themselves as an investment that can improve the overall risk/return structure
of a portfolio of investments. Market neutral funds should not be confused
with Long/Short investment strategies (see below). The key feature of market
neutral funds are the low correlation between their returns and the traditional
asset's.

Event Driven Funds

Event driven funds seek to make profitable investments
by investing in a timely manner in securities that are presently affected
by particular events. Such events include distressed debt investing,
merger arbitrage (sometimes called risk arbitrage) and corporate
spin-offs and restructuring.

Long/Short Funds

Funds employing long/short strategies generally invest
in equity and fixed income securities taking directional bets on
either an individual security, sector or country level. For example, a
fund might do pairs trading, and buy stocks that they think will
move up and sell stocks they think will move down. Or go long sectors they
think will go up and short countries they think will go down. Long/Short
strategies are not automatically market neutral. That is, a long/short
strategy can have significant correlation with traditional markets, and
surprisingly have seen large down turns in exactly the same times as major
market downturns. For example, Pension & Investments reported on November
30, 1998:

Many long-short managers, which aim to profit from going
long on stellar stocks and selling short equity albatrosses, typically
use traditional stock valuation factors such as price-to-earnings and price-to-bok
value ratios in their mathematical models to cull the winners from the
losers. Unfortunately for them, when the market ran into turbulence in
late July and August, investors sought safe haven in some of the largest-but
expensive-stocks that these models had rejected as overpriced.

Then, after the Federal Reserve Bank began easing interest
rates in late September, investors rushed to buy small-capitalization,
high-octane stocks that had been neglected in favor of large cap stocks
for most of the year. ... As a result, some market long-short managers
got hit with a double-whammy.

Tactical Trading

Quoting from "Hedge Funds Demystified":

Tactical trading refers to strategies that speculate on
the direction of market prices of currencies, commodities, equities and/or
bonds. Managers typically are either systematic or discretionary. Systematic
managers are primarily trend followers who rely on computer models based
on technical analysis. Discretionary managers usually take a less quantitative
approach and rely on both fundamental and technical analysis. This is the
most volatile sector in terms of performance because many managers combine
long and/or short positions with leverage to maximize returns...

The Hedge Fund Industry and Quantitative Methods

Quantitative methods have been successfully applied in
the hedge fund industry to improve returns, and control risk. That said,
there have been striking failures of seemingly quantitatively driven funds
(such as Long-Term Capital). Some of the most quantitatively driven strategies
occur in the Market Neutral/Relative Value Sector of the Hedge Fund World,
so we will exam this sector in more detail by discussing some of the specific
types of strategies they employ. The following is a list of important and
quantitatively driven market neutral/relative value strategies. I refer
you to "Hedge Funds Demystified" for a detailed description of
each:

Fixed income arbitrage

Covertible bond arbitrage

Mortgage backed security arbitrage

Derivatives Arbitrage

Market Neutral Long/Short Equity Strategies

Hedge Fund Returns

As hedge funds are often viewed as providing returns that
are "cheap" relative to risk, their performance is usually evaluated
on a risk-adjusted return basis. The common number that is quoted is the
Sharpe Ratio which is the ratio of annualized excess returns to
the annualized standard deviation of returns. The following repeats the
data in Table 7 of "Hedge Funds Demystified" and gives an idea
of the relative performance of hedge funds compared with some standard
indexes over the period January 1993 - December 1997. The table represents
returns on each Hedge Fund Sector, that is, the returns and standard deviations
in each column represents the returns that were realized on an equal weighted
investment portfolio of all the hedge funds in a given sector.

Market Neutral Funds (38 Funds)

Event Driven Funds (49 Funds)

Equity Long/Short (89 Funds)

Tactical Trading (101 Funds)

S&P 500

FT/S&P Actuaries World (USD Perspective)

Lehman Aggregate Bond Index

Compound Return

13.37%

17.25%

19.29%

19.48%

20.25%

15.18%

7.48%

Standard Deviation

1.86%

3.12%

7.20%

9.97%

10.66%

10.88%

4.14%

Sharpe Ratio

4.69

4.05

2.07

1.54

1.52

1.03

.7

Leverage

The final point of this lecture is the notion of leverage
in hedge funds. Leverage has many different precise definitions, but all
of them attempt to measure the amount of assets being funded by each investment
dollar. Leverage, especially in the days following the Long-Term Capital
bailout, has been in the press a lot. There are two fundamentally different
ways of measuring leverage:

Total long market value divided by total investment capital

Total long market value plus total short market value
divided by investment capital

Consider two fictitious funds with the following investments

FUND A

FUND B

Long

Short

Long

Short

$100

$0

$100

$100

Suppose each fund has $10 of investment capital. First of all, fund
A is leverage 10 to 1 in either definition of leverage, while fund B is
leveraged 10 to 1 in the first definition, but 20 to 1 in the second. What
are the risks in holding each fund?

First, let's examine the risks we can enumerate:

Fund A: for every dollar of downward movement the Long position
moves, the fund loses 10% of its capital. That is, for every 1% move in
the long market value, there is a 10% move in the value of investment capital.

Fund B: for every dollar movement in either the long market
value or the short market value, there is a 10% change in the value of
investment capital.

Thus, from one point of view, the position of Fund B might be regarded
as more risky than the position of Fund A. Why? Because Fund B has essentially
$200 of potential market movements available, while Fund A only has $100.
But, suppose the short position in fund B is actually a hedge against
the movement of the long position. That is, suppose the short position
is highly correlated with the long position so that the short position
is risk-reducing relative to the long position. In this case, the
risk of fund B may be regarded as less than the risk of fund A. An immediate
conclusion of this example is that it is difficult to assess from leverage
alone the level of risk inherent in a fund. To form a more accurate understanding
of risk requires an understanding of the distribution of future returns
of a fund.

Put another way, the information we provide here cannot in itself adequately
express the risk of the fund. So, then, why don't people look at the risk
of funds (e.g., Value at Risk or some other risk measure) and forget about
leverage altogether? Why do investors and the press worry about leverage
so much these days? The answer is that risk is deceptively difficult to
measure. Consider for example a highly leveraged fund that is long and
short securities that are highly correlated. Moreover, assume that this
correlation is measured using historical data, and that the fund is regarded
as only moderately risky due to the presumed stability of return correlations.
If the fund is highly leveraged and it turns out that the correlation assumptions
are incorrect, then the damage of the incorrect analysis will be severe
precisely due to the miscalculation in the correlations. Put another way,
the damage of a mis-estimate of risk is itself leveraged when the fund
is leveraged.